Finite Group Databasebeta

← #14769230

Subgroups — #14769230

Order 2816.

1490 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623257C211yesmaximal, characteristic
2C2×C8×D44C211yesmaximal, characteristic, complemented
3C2×#10622417C212yesmaximal, complemented
4#13071567C211yesmaximal, characteristic, complemented
5#13069540C211yesmaximal, characteristic, complemented
6#13069036C212yesmaximal, complemented
7#13068925C212yesmaximal, complemented
8#13068613C211yesmaximal, characteristic, complemented
9#13068555C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic, complemented
11C11×#1956C211yesmaximal, characteristic, complemented
12C22×#4343C2212yes—
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×#66999C2212yes—
15C22×C8×D11C2212yes—
16#10623257—24no—
17#10623257C418yescomplemented
18C2×#66948—21no—
19C2×#66947—22no—
20C2×#66945C2212yes—
21C2×C4⋊C4×D11—21no—
22C2×C4×D44C2211yescharacteristic
23C2×C4×D44C2211yescharacteristic
24C2×C11×#103C2212yes—
25C2×C11×#103C2212yes—
26C2×C4×C8×C11C2211yescharacteristic
27C11×#384C2211yescharacteristic
28C2×#66899C2212yes—
29C2×#66899C2212yes—
30C2×#66885C2211yescharacteristic
31C2×#66885C2211yescharacteristic
32C2×(C2×D11)⋊C8C2212yes—
33#10622603—22no—
34#10622601—21no—
35#10622600C2212yes—
36C4⋊C4×Dic11—21no—
37C2×#66873C2212yes—
38C4×C4⋊Dic11C2211yescharacteristic
39C2×C4⋊(C11⋊C8)C2211yescharacteristic
40#10622417—28no—
41C8×D44—24no—
42#10622189C2211yescharacteristic
43#10622189C2211yescharacteristic
44#10622167C2212yes—
45C22×Q8×C11C2312yes—
46C2×#4343—24no—
47C2×#4343—24no—
48C2×#4343—24no—
49C2×#4343—42no—
50C2×#4343—42no—
51C2×#4343C2×C418yes—
52C22×D44—22no—
53C22×D44D411yescharacteristic
54C22×D44C2311yescharacteristic
55C22×C4×D11—21no—
56C22×C4×D11—22no—
57C22×C4×D11C2312yes—
58C22×C8×C11C2311yescharacteristic
59C22×C8×C11C2311yescharacteristic
60C11×C4⋊Q8—22no—
61C11×C4⋊Q8C2×C414yes—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—21no—
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11C2311yescharacteristic
68#66999—24no—
69#66999C2×C418yes—
70C2×(C2×D11)⋊C4—22no—
71C2×(C2×D11)⋊C4—21no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—22no—
74C2×(C2×D11)⋊C4D412yes—
75C2×C4⋊Dic11D411yescharacteristic
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4⋊Dic11C2311yescharacteristic
79C2×Dic11⋊C4—22no—
80C2×C4×Dic11—21no—
81C2×C4×Dic11—22no—
82C22×C11⋊C8C2312yes—
83C2×C8×D11—24no—
84C2×C8×D11—24no—
85C2×C8×D11—42no—
86#66948—28no—
87#66947—216no—
88#66945—24no—
89#66945—42no—
90C4⋊C4×D11—28no—
91C4×D44—22no—
92C4×D44C2×C414yes—
93C4×D44C2×C414yes—
94C4×D44D414yes—
95C11×#103—24no—
96C11×#103—42no—
97C4×C8×C11—22no—
98#66899—24no—
99#66899—42no—
100C11⋊#95—21no—
101C11⋊#95—22no—
102#66885—22no—
103#66885D414yescomplemented
104(C2×D11)⋊C8—24no—
105#66873—24no—
106C4⋊(C11⋊C8)—22no—
107#22417—111nomaximal, Sylow
108C23×D11—21no—
109C23×D11C2×D412yes—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C22×C414yes—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11C2×D412yes—
125#4343—216no—
126#4343—48no—
127#4343—48no—
128#4343—48no—
129C2×D44—28no—
130C2×D44—22no—
131C2×D44—22no—
132C2×D44—21no—
133C2×D44—21no—
134C2×D44—21no—
135C2×D44—44no—
136C2×D44—44no—
137C2×D44C22⋊C414yes—
138C2×D44C22×C412yes—
139C2×D44C2×D412yes—
140C2×D44#4112yes—
141C2×C4×D11—28no—
142C2×C4×D11—24no—
143C2×C4×D11—22no—
144C2×C4×D11—22no—
145C2×C4×D11—22no—
146C2×C4×D11—22no—
147C2×C4×D11—44no—
148C2×C4×D11—44no—
149C2×C4×D11—42no—
150C2×C4×D11—42no—
151C2×C4×D11C22×C414yes—
152C2×C4×D11C2×D414yes—
153C2×C8×C11—21no—
154C2×C8×C11—21no—
155C2×C8×C11—21no—
156C2×C8×C11—21no—
157C2×C8×C11—21no—
158C2×C8×C11C2×D412yes—
159C11×C4⋊C4—24no—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4—42no—
164C11×C4⋊C4—81no—
165C42×C11C22×C412yes—
166C42×C11C2×D412yes—
167(C2×D11)⋊C4—28no—
168(C2×D11)⋊C4—24no—
169(C2×D11)⋊C4—44no—
170(C2×D11)⋊C4—82no—
171(C2×D11)⋊C4C22⋊C418yes—
172C4⋊Dic11—21no—
173C4⋊Dic11—21no—
174C4⋊Dic11—21no—
175C4⋊Dic11—21no—
176C4⋊Dic11C22⋊C414yes—
177C4⋊Dic11C22×C412yes—
178C4⋊Dic11C2×D412yes—
179Dic11⋊C4—28no—
180C4×Dic11—44no—
181C4×Dic11—42no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—22no—
185C8×D11—48no—
186C2×#547—111no—
187C2×C8×D4—111no—
188C2×#416—112no—
189#2354—111no—
190#1981—111no—
191#1956D1111yescharacteristic, complemented
192#1892—112no—
193#1873—112no—
194#1802—111no—
195#1788—112no—
196C4×#102—111no—
197C23×C11C22×D411yescharacteristic
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—41no—
208C22×D11—41no—
209C22×D11—41no—
210C22×D11—41no—
211C22×D11C2×C22⋊C414yes—
212Q8×C11—24no—
213Q8×C11—24no—
214Q8×C11—42no—
215Q8×C11—42no—
216C2×C4×C11—21no—
217C2×C4×C11—21no—
218C2×C4×C11—24no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—42no—
224C2×C4×C11C2×C22⋊C412yes—
225C2×C4×C11C2×C22⋊C412yes—
226C2×C4×C11#13512yes—
227C2×C4×C11#13512yes—
228C2×C4×C11C23×C411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11H(5,𝔽2)11yescharacteristic
233C2×C4×C11H(5,𝔽2)11yescharacteristic
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—41no—
239C2×Dic11—41no—
240C2×Dic11—41no—
241C2×Dic11—41no—
242C2×Dic11—41no—
243C2×Dic11—41no—
244C2×Dic11—41no—
245C2×Dic11C2×C22⋊C414yes—
246D44—22no—
247D44—22no—
248D44—22no—
249D44—28no—
250D44—416no—
251D44C4×D414yes—
252C4×D11—24no—
253C4×D11—24no—
254C4×D11—24no—
255C4×D11—24no—
256C4×D11—416no—
257C4×D11—48no—
258C8×C11—22no—
259C8×C11—41no—
260C11⋊C8—42no—
261C22×#41—112no—
262C23×C8—112no—
263#547—118no—
264#547—224no—
265C2×C4⋊Q8C2×D1111yescharacteristic
266C2×#123—222no—
267C2×C22⋊Q8—112no—
268C2×#121—221no—
269C2×C4×D4—111no—
270C2×C4×D4—111no—
271C2×#117—112no—
272C22×C4⋊C4—221no—
273C8×D4—224no—
274C2×C4⋊C8—111no—
275#416—228no—
276C2×#103—112no—
277C2×#103—112no—
278C2×#103C2×D1112yes—
279C2×#103C2×D1112yes—
280C2×#102—111no—
281C2×#102—111no—
282C2×#102—112no—
283C2×C22⋊C8—112no—
284C2×C4×C8C2×D1111yescharacteristic
285#390—221no—
286#388—222no—
287#384C2×D1111yescharacteristic
288#380—112no—
289C4×C4⋊C4—111no—
290C4×C4⋊C4—221no—
291#340—111no—
292#340—111no—
293#340—112no—
294C22×C11C22×C22⋊C411yescharacteristic
295C22×C11D4211yescharacteristic
296C22×C11#54611yescharacteristic
297C22×C11C2×#13511yescharacteristic
298C22×C11C2×#13511yescharacteristic
299C22×C11#57711yescharacteristic
300C22×C11#57811yescharacteristic
301C2×D11—24no—
302C2×D11—24no—
303C2×D11—24no—
304C2×D11—24no—
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—42no—
315C4×C11—22no—
316C4×C11—44no—
317C4×C11—82no—
318C4×C11#41614yescomplemented
319C4×C11C2×C4×D411yescharacteristic
320C4×C11#51811yescharacteristic
321C4×C11D4211yescharacteristic
322C4×C11#54611yescharacteristic
323Dic11—24no—
324Dic11—42no—
325Dic11—42no—
326Dic11—81no—
327C2×#41—118no—
328C2×#41—224no—
329C2×#41—224no—
330C2×#41—224no—
331C2×#41—442no—
332C2×#41—442no—
333C22×Q8C22×D1112yes—
334C22×D4—111no—
335C22×D4—111no—
336C22×D4—222no—
337C23×C4—112no—
338C23×C4—222no—
339C23×C4—221no—
340C22×C8—112no—
341C22×C8—224no—
342C22×C8—224no—
343C22×C8—442no—
344C22×C8C22×D1111yescharacteristic
345C22×C8C22×D1111yescharacteristic
346C4⋊Q8—22no—
347C4⋊Q8C4×D1114yes—
348#123—2216no—
349C22⋊Q8—118no—
350C22⋊Q8—224no—
351#121—228no—
352C4×D4—114no—
353C4×D4—114no—
354C4×D4—114no—
355C4×D4—222no—
356#117—224no—
357#117—442no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—111no—
363C2×C4⋊C4—111no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—111no—
366C2×C4⋊C4—228no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4C22×D1112yes—
369C2×C22⋊C4—112no—
370C2×C22⋊C4—222no—
371C2×C22⋊C4—221no—
372C2×C22⋊C4—222no—
373C2×C22⋊C4—222no—
374C2×C42—222no—
375C2×C42—221no—
376C2×C42C22×D1111yescharacteristic
377C4⋊C8—222no—
378#103—24no—
379#103—42no—
380#103—224no—
381#103—442no—
382#102—114no—
383#102—224no—
384#102—222no—
385C22⋊C8—224no—
386C4×C8—22no—
387#95—222no—
388#95—221no—
389C2×C11D4×C22⋊C411yescharacteristic
390C2×C11C2×#41611yescharacteristic
391C2×C11#289811yescharacteristic
392C2×C11#328311yescharacteristic
393C2×C11#328411yescharacteristic
394C2×C11#330211yescharacteristic
395C2×C11#330311yescharacteristic
396D11—44no—
397D11—44no—
398C24—112no—
399C24—221no—
400#41—2216no—
401#41—448no—
402#41—448no—
403#41—448no—
404C2×Q8—22no—
405C2×Q8—22no—
406C2×Q8—22no—
407C2×Q8—22no—
408C2×Q8—22no—
409C2×Q8C2×C4×D1114yes—
410C2×D4—114no—
411C2×D4—112no—
412C2×D4—112no—
413C2×D4—112no—
414C2×D4—228no—
415C2×D4—222no—
416C2×D4—222no—
417C2×D4—221no—
418C2×D4—221no—
419C2×D4—221no—
420C2×D4—444no—
421C2×D4—444no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—112no—
425C22×C4—114no—
426C22×C4—114no—
427C22×C4—228no—
428C22×C4—222no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—221no—
433C22×C4—221no—
434C22×C4—224no—
435C22×C4—221no—
436C22×C4—444no—
437C22×C4—444no—
438C22×C4—442no—
439C22×C4—442no—
440C22×C4D4×D1111yescharacteristic
441C22×C4D4×D1111yescharacteristic
442C22×C4C23×D1111yescharacteristic
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—222no—
449C2×C8—222no—
450C2×C8—222no—
451C2×C8—448no—
452C2×C8D4×D1112yes—
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—42no—
458C4⋊C4—81no—
459C4⋊C4—114no—
460C4⋊C4—112no—
461C4⋊C4—112no—
462C4⋊C4—228no—
463C4⋊C4—221no—
464C4⋊C4—221no—
465C4⋊C4—221no—
466C4⋊C4—221no—
467C22⋊C4—118no—
468C22⋊C4—228no—
469C22⋊C4—224no—
470C22⋊C4—444no—
471C22⋊C4—882no—
472C42—444no—
473C42—442no—
474C42C2×C4×D1112yes—
475C42D4×D1112yes—
476C11#2241711yescharacteristic, complemented, Sylow
477C23—114no—
478C23—222no—
479C23—222no—
480C23—222no—
481C23—222no—
482C23—222no—
483C23—222no—
484C23—222no—
485C23—222no—
486C23—222no—
487C23—441no—
488C23—441no—
489C23—441no—
490C23—441no—
491C23C2×D4×D1111yescharacteristic
492Q8—24no—
493Q8—24no—
494Q8—42no—
495Q8—42no—
496D4—114no—
497D4—222no—
498D4—222no—
499D4—222no—
500D4—228no—
501D4—4416no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—24no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—42no—
509C2×C4—42no—
510C2×C4—114no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—222no—
518C2×C4—222no—
519C2×C4—4416no—
520C2×C4—441no—
521C2×C4—441no—
522C2×C4—441no—
523C2×C4—441no—
524C2×C4—448no—
525C2×C4—441no—
526C2×C4—441no—
527C2×C4—441no—
528C2×C4C22⋊C4×D1112yes—
529C2×C4C22⋊C4×D1112yes—
530C2×C4#6696912yes—
531C2×C4#6697212yes—
532C2×C4C22×C4×D1111yescharacteristic
533C2×C4C2×D4×D1111yescharacteristic
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4#6703711yescharacteristic
536C2×C4#41×D1111yescharacteristic
537C2×C4#6704211yescharacteristic
538C8—22no—
539C8—41no—
540C8—442no—
541C22—224no—
542C22—224no—
543C22—224no—
544C22—224no—
545C22—442no—
546C22—442no—
547C22—442no—
548C22—442no—
549C22—442no—
550C22—442no—
551C22—442no—
552C22—442no—
553C22—442no—
554C22—442no—
555C22C2×C22⋊C4×D1111yescharacteristic
556C22#1062320711yescharacteristic
557C22#1062324811yescharacteristic
558C22C2×#6696911yescharacteristic
559C22#1062329311yescharacteristic
560C22C2×#6697211yescharacteristic
561C22#1062329711yescharacteristic
562C4—22no—
563C4—44no—
564C4—82no—
565C4—224no—
566C4—442no—
567C4—442no—
568C4—881no—
569C4#1062241714yescomplemented
570C4C4×D4×D1111yescharacteristic
571C4#1062307611yescharacteristic
572C4#1062314011yescharacteristic
573C4#1062314311yescharacteristic
574C2—444no—
575C2—444no—
576C2#1307143711yescharacteristic
577C2C2×#1062241711yescharacteristic
578C2#1307714411yescharacteristic
579C2#1308033611yescharacteristic
580C2#1308034511yescharacteristic
581C2#1308053211yescharacteristic
582C2#1308054311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1956C2
socleC23×C11C22×D4
prime radicalC2×#10623257C2
cosocleC22×C4×C11C24
hypercenter#1956D11
hypocenterC11#22417
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1956

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C8×D44C2semidirect
3. C2×#10622417C2semidirect
4. #13071567C2semidirect
5. #13069540C2semidirect
6. #13069036C2semidirect
7. #13068925C2semidirect
8. #13068613C2semidirect
9. #13068555C2semidirect
10. C4×#66885C2semidirect
11. C11×#1956C2semidirect
17. #10623257C4semidirect
103. #66885D4semidirect
191. #1956D11semidirect
318. C4×C11#416semidirect
476. C11#22417semidirect
569. C4#10622417semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106232572
C2×C8×D442
C2×#106224172
#130715672
#130695402
#130690362
#130689252
#130686132
#130685552
C4×#668852
C11×#19562
#2241711